Departement de Mathematique d'Orsay
Département de Mathématiques d'Orsay
Amaury Freslon
Université Paris-Saclay
Institut de Mathématique d'Orsay - Bâtiment 307
91405 Orsay Cedex

Courrier électronique :
Bureau : 2L22 Bât. 307

I am currently Maître de Conférence at Université Paris-Sud in the Topology and dynamics team. I am interested in the study of topological quantum groups, their structure and properties. I am also a member of the ANR projects AODynG and Noncommutative Analysis on Groups and Quantum Groups.

Here is my CV in english and in french.

Si vous cherchez ma page d'enseignement, elle se trouve ici.


  • Classical actions of quantum permutation groups (with F. Taipe and S. Wang), Arxiv preprint pdf.
  • Abstract


  1. Tannaka-Krein reconstruction and ergodic actions of easy quantum groups (with F. Taipe and S. Wang) Comm. Math. Phys. 399 (2023), 105-172 : link and pdf (old version).
  2. Abstract
  3. The Gaussian part of a compact quantum group (with U. Franz and A. Skalski), J. Geom. Phys. 184 (2023), 104710 : link and pdf (old version).
  4. Abstract
  5. Free wreath products with amalgamation, Comm. Alg. 51 (2023), no 1, 72-94 : link and pdf (old version).
  6. Abstract
  7. Cutoff profiles for quantum Lévy processes and quantum random transpositions (with L. Teyssier and S. Wang), Probab. Theory Related Fields 183 (2022), 1285-1327: link and pdf (old version).
  8. Abstract
  9. On the classification of partition quantum groups, Exp. Math. 39 (2021), no 2, 238-270 : link and pdf (old version).
  10. Abstract
  11. Positive definite functions and cut-off for discrete groups, to appear in Canad. Math. Bull. 64 (2021), no 2, 306-322 : link and pdf.
  12. Abstract
  13. Topological generation and matrix models for quantum reflection groups (with M. Brannan and A. Chirvasitu), Adv. Math. 363 (2020) : link and pdf.
  14. Abstract
  15. On two-coloured noncrossing partition quantum groups, Trans. Amer. Math. Soc. 372 (2019), no 6, 4471-4508 : link and pdf (old version).
  16. Abstract
  17. On the representation theory of some noncrossing partition quantum groups, Algebr. Represent. Theory. 23 (2019), no 3, 483-492 : link and pdf (old version).
  18. Abstract
  19. Quantum reflections, random walks and cut-off, Internat. J. Math. 29 (2018), no 14, 1850101 : link and pdf (old version).
  20. Abstract
  21. Cut-off phenomenon for random walks on free orthogonal quantum groups, Probab. Theory Related Fields 174 (2019), no3-4, 731-760 : link and pdf (old version).
  22. Abstract
  23. Torsion and K-theory for some free wreath products (with R. Martos), Int. Math. Res. Not. 2020 (2020), no 6, 1639-1670 : link and pdf (old version).
  24. Abstract
  25. Modelling questions for quantum permutations (with T. Banica), Infin. Dimens. Anal. Quantum Probab. Relat. Top. 21 (2018), no 2, 1-26 : link and pdf (old version).
  26. Abstract
  27. The radial MASA in free orthogonal quantum groups (with R. Vergnioux), J. Funct. Anal. 271 (2016), no 10, 2776-2807: link and pdf (old version).
  28. Abstract
  29. Wreath products of finite groups by quantum groups (with A. Skalski), J. Noncommut. Geom. 12 (2018), no 1, 29-68 : link and pdf (old version).
  30. Abstract
  31. On the partition approach to Schur-Weyl duality and free quantum groups (with an appendix by A. Chirvasitu), Transform. Groups 22 (2017), no 3, 707-751 : link and pdf (old version).
  32. Abstract
  33. On bi-free De Finetti theorems (with M. Weber), Ann. Math. Blaise Pascal 23 (2016), no 1, 21-51 : link and pdf (old version).
  34. Abstract
  35. Permanence of approximation properties for discrete quantum groups, Ann. Inst. Fourier 65 (2015), no 4, 1437-1467 : link and pdf (old version).
  36. Abstract
  37. Fusion (semi)rings arising from quantum groups, J. Algebra 417 (2014), 161-197 : link and pdf (revised version).
  38. Abstract
  39. On the representation theory of partition (easy) quantum groups (with M. Weber), J. Reine Angew. Math. 720 (2016), 155-197 : link and pdf (old version).
  40. Abstract
  41. Graphs of quantum groups and K-amenability (with P. Fima), Adv. Math. 260 (2014), 233-280 : link and pdf (old version).
  42. Abstract
  43. CCAP for universal discrete quantum groups (with K. De Commer and M. Yamashita, with an appendix by S. Vaes), Comm. Math. Phys. 331 (2014), no 2, 677-701 : link and pdf (old version).
  44. Abstract
  45. Examples of weakly amenable discrete quantum groups, J. Funct. Anal. 265 (2013), no 9, 2164-2187 : link and pdf (old version).
  46. Abstract
  47. A note on weak amenability for free products of discrete quantum groups, C. R. Acad. Sci. Paris 350 (2012), no 7-8, 403-406 : link and pdf (old version).
  48. Abstract


  • Compact matrix quantum groups and their combinatorics, LMS Student Texts in Mathematics 106, Cambridge University Press (2023) : link .


  1. On the classification of non-crossing partition quantum groups, Oberwolfach reports 45 (2019).
  2. Cut-off for quantum random walks, Oberwolfach reports 22 (2018).


  • Études des groupes quantiques libres : Analyse, Algèbre et Probabilités, Habilitation à diriger des recherches (Habilitation thesis) : pdf and slides.
  • Approximation properties for discrete quantum groups (PhD thesis) : pdf.
  • Abstract


  1. Mathématiques, exercices incontournables - MPSI/MP2I (3ème edition) (avec M. Bages, P. Bernard, J. Freslon, M. H&eactute;zard, C. Lagrange, J. Levie, M. Mansuy et J. Poineau), Dunod (2023) : lien.
  2. Mathématiques, exercices incontournables - PCSI/PTSI (3ème edition) (avec M. Bages, P. Bernard, J. Freslon, M. H&eactue;zard, C. Lagrange, J. Levie, M. Mansuy et J. Poineau), Dunod (2023) : lien.

Other documents

  • Slides (in english) from a talk on Easy quantum actions.
  • Slides (in english) from a talk on Quantum groups in the heat.
  • Slides (in english) from a talk on How to (badly) quantum shuffle cards.
  • Slides (in english) from a talk on Diffusion of quantum orthogonal Brownian motion.
  • Notes (in english) from a lecture series on The classification of partition quantum groups.
  • Notes (in english) from a talk on Classical spaces and quantum symmetries.
  • Notes (in english) from a talk on the Cut-off for quantum random walks.
  • Notes (in french) from a talk on Partition algebras and free quantum groups.
  • Notes (in french) from a talk on Approximation properties for quantum groups.
  • An introduction (in french) to the Elliott program.
  • An introduction (in french) to C*-simplicity.
  • An exposition (in english) of the Ergodic theorem for compact groups.
  • An exposition (in french) of A. Connes' result on the fundamental group of a property (T) factor.

Département de Mathématiques
, Université Paris-Sud, Bât. 425, F-91405 Orsay Cedex ,France